It was only natural that my thoughts on knowledge and subsequent realizations would extend to the consideration of alternative ways to engineer understanding and thus, descriptions.
The drive of this work is a found connection between ontologies — one of the formal ingredients† of descriptions — and distinctions.
To put it simply, ontologies are a conceptual vocabulary; a listing of primitives one uses in forging statement about things. My thesis is that, there is an order to be found in ontologies and that order is the product of underlying distinctions.
What I am trying to do here is attempt to find a pattern in a process which for most part evolved naturally — referring to both Language and Knowledge. Things seemed to be discovered as we go and structured out of necessity.
I am framing that necessity as being the manifestation of a rule or a law we are bound by in the knowledge-making.
Beyond its primary task of supporting my thesis, I believe this essay to be a crucial step to the proposal of an ontological calculus which I think is one possible way to crystallize these insights into a working technology. The converging point of my studies on both knowledge and tensors.
In what follows, I will argue from scratch how my thesis ought to hold and then proceed in exploring its implications with a practical case.
As this work falls within the context of the above mentioned vision, it seems only reasonable to start this discussion from the requirements of fulfillment.
The possibility of finding a method or a technique within an existing body of knowledge is bound to both its structure and the adequacy of its representation. If a technology is found then the seed of its possibility was always there. We are unable to see it at first because things weren’t in the right format and did not emphasis the right aspect.
Employing this insight, we can actively seek the right representation to meet our end instead of stumbling upon a tech as a byproduct of another process. And I believe that the representation induced by “dissolving knowledge into distinctions” might be the right setup.
Thus, we just need to identify constructs in descriptive knowledge that can lend themselves to a certain calculus.
Descriptions either induce or imply a base ontology of sorts. Whether constructed or evolved from natural usage and metaphoric‡‡ import, wherever there is knowledge there is an ontology to be found.
Such construct provides us with the conceptual primitives and linguistic bits that will form all our subsequent descriptions and reasoning — proposed to be an instance of calculus† — within a field of interest.
Ontology seems to be a good starting point.
I also held the thesis in a previous piece‡ that knowledge is nothing but the art of drawing distinctions. They are the fundamental to understanding; in fact, they are the reason we have understanding at all. As ignorance is, the absence of distinction.
When one expresses understanding, it comes in the form of descriptions.
From one side we have that, ontologies provide with the ingredients of description and from the other, distinctions are the reason one can describe things as a demonstration of understanding. Bringing things together, ontologies and distinctions must be related.
Given the order of their occurrence, that is, distinctions exist at the low level — hinting to a computer science analogy — while ontologies are as close as it gets to descriptions (high level).
I propose that, distinctions are generators of ontologies.
An ontology is a principled listing of primitives and categories. These can be derived as a product of basic distinctions. Their combinations reproduce in-theory the full ontological lattice, that is, all that is allowed and described by the body of knowledge.
My study of distinctions††, leaves us with two important conclusions: (a) the concept of “Thing” is primary in the sense that anything else is an instance of it and, (b) distinctions are either two — fold (diad) and three — fold (triad).
We can construct a generic ontology — combining (a) and (b) — by applying fundamental distinctions to the primary category, Thing. In our case, I will employ three distinctions studied in††.
— Quine’s Concrete vs. Abstract.
— Whitehead’s Continuant vs. Occurrent.
— Peirce’s Independent — Relative — Mediating progression.
These primitives and their derivations are good enough to reproduce a number of very familiar categories that are part of our everyday use.
The procedure is quite simple. Each distinction provides us with primitives which we combine so that each combination produces a category. The result is exposed in a lattice as shown below.
A — Quine x Whitehead
B — Whitehead x Peirce
C — Peirce x Quine
D — All at once
The product of merely three distinctions produced a total of 28 categories. Most of them are familiar notions like, Form, Object, History, Situation, etc.
It is obvious that further distinctions will make this construction grow exponentially. But it is safe to conjecture that to the limit where one includes all of his acquired distinctions then the resulting categories must encompass in-principle all of one’s descriptive power.
Reducibility Conjecture — the full knowledge content can be reduced in term of distinctions to be made about its object.
An important assumption we made in this process is that the order in which the combination happens does not matter, i.e. Concrete Occurrent = Occurrent Concrete.
A direct consequence of this operational feature is that, relations must close. That is, if two bring a third then the third combined with either of them must hint to the remaining one. Furthermore, all of three must hint to an invariant fourth which supposed to represent the connection among all of them.
This reasoning lead me to consider a category of the D — product as a triangulation of the (A, B, C) — products.
Taking the first triangulation as an example, I read : “An Object is an Observable Entity considered as to its Actuality.” Although this scheme of definition doesn’t apply to all triangulations and may vary for reasons that will be clear later. It is satisfying to find that results reconnect after branching from the same principle.
“Closure is good.” — Self.
Please note that this aspect even though appealing is probably an artifact of my initial choice — 3 distinctions leading to triangulations. Generalizations of the same idea to a different number of distinctions are to be explored.
One should remember that the word we associate to a product of distinctions is just a label for a meaning that is primarily provided by the distinctions and their relationships. Categories acquire meaning through this derivation process.
Avoid being deceived by the words and focus on the distinctions behind them.
I’d like to bring to your attention that, one is perfectly capable of selecting a certain category as his prime concept and then branch from it. This way of locally applying distinctions is particularly useful when dealing with big lattices.
A quick example. By taking the Object category and applying Kant’s three-fold Thesis-Antithesis-Synthesis progression, we obtain something that would instantiate to, particle, antiparticle and carrier. Something known to any Physics enthusiasts.
Feel free to share connections you made as commentaries.
One must be careful in dealing with those labels as sometimes the closest word to the meaning could just an instance of the category and thus doesn’t possess the generality to subsume all the remaining instances. This is not surprising as it is an expected backfire from an attempt to formalize something which for most parts evolved naturally.
The comprehensive aspect of a formalization makes use realize that our language might lack generic identifiers or even that we didn’t map certain conceptual regions . Thus when facing these issues our mind attempt to fill the blanks with the closest notion we know of. The best solution is to come with a new word to avoid any confusion that arises from the usage of an established word which comes with contextual modes of usage.
What I am trying to say through the previous 2 paragraphs is that the names I was inspired to use for the categories aren’t definitive in any sense. They are approximates where some of them do a good job implying the meaning they are supposed to hold and others might exhibit the intended meaning only in certain situations.
To illustrate my point, let’s take the Object category whose instances can be pretty much anything around you. Our language evolved in a way where it can even refer to abstract things. Thus, the word “object” is to some extent an inefficient labeling of combination Independent-Concrete-Continuant. We still accept it because we recognize that the objectification of abstract and virtual thing is nothing but a metaphoric extensions‡‡ of a realization made initially in the physical world.
At the end of the day, the composition of distinctions is all that matters. As they are the generators of knowledge.